Problem: $A$ $B$ $C$ If: $ BC = 4x + 7$, $ AB = 5x + 7$, and $ AC = 32$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {5x + 7} + {4x + 7} = {32}$ Combine like terms: $ 9x + 14 = {32}$ Subtract $14$ from both sides: $ 9x = 18$ Divide both sides by $9$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 4({2}) + 7$ Simplify: $ {BC = 8 + 7}$ Simplify to find ${BC}$ : $ {BC = 15}$